Thank you for your response. Can the p-values be calculated manually in the same manner as a Pearson correlation (based only on sample size and magnitude of the correlation)? Basically, if we want to report these values in a paper, what are we to indicate regarding significance of the correlations?

No, it's more involved when it comes to these model-estimated correlations. One way to get this is to parameterize your model so that latent variables have variances 1, in which case their covariance parameters are correlations and you get the SEs.